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r = \frac{5\sqrt2}2 - AMAZONAWS
r = \frac{5\sqrt2}2 - AMAZONAWS
📅 March 11, 2026
👤 scraface
Mar 11, 2026
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📌 x^3 + y^3 = 1728 - 3(32)(12) = 1728 - 1152 = 576
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📌 Next, $5^1 = 5$, $5^2 = 25 \equiv 1 \pmod{8}$, so powers of 5 mod 8 also cycle every 2: $5, 1, 5, 1, \dots$
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📌 Compare \( S_n = 3^n - 1 \) with the geometric sum formula. This suggests \( r = 3 \) and \( a = 2 \), since \( 3^n - 1 = 2 \cdot \frac{3^n - 1}{3 - 1} \).
